Lattice-BGK approach to simulating granular flows

Many continuum theories for granular flow produce an equation of motion for the fluctuating kinetic energy density (granular temperature) that accounts for the energy lost in inelastic collisions. Apart from the presence of an extra dissipative term, this equation is very similar in form to the usual temperature equation in hydrodynamics. It is shown how a lattice-kinetic model based on the Bhatnagar-Gross-Krook (BGK) equation that was previously derived for a miscible two-component fluid may be modified to model the continuum equations for granular flow. This is done by noting that the variable corresponding to the concentration of one species follows an equation that is essentially analogous to the granular temperature equation. A simulation of an unforced granular fluid using the modified model reproduces the phenomenon of clustering instability, namely the spontaneous agglomeration of particles into dense clusters, which occurs generically in all granular flows. The success of the continuum theory in capturing the gross features of this basic phenomenon is discussed. Some shear flow simulations are also presented.     

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

The evolution with β of the distributions of the spacing ‘s’ between nearest-neighbour levels of unfolded spectra of random matrices from the β-Hermite ensemble (β-HE) is investigated by Monte Carlo simulations. The random matrices from the β-HE are real symmetric and tridiagonal where β, which can take any positive value, is the reciprocal of the temperature in the classical electrostatic interpretation of eigenvalues. The distribution of eigenvalues coincide with those of the three classical Gaussian ensembles for β=1, 2, 4. The use of the β-HE ensemble results in an incomparable speed up and efficiency of numerical simulations of all spectral characteristics of large random matrices. Generalized gamma distributions are shown to be excellent approximations of the nearest-neighbor spacing (NNS) distributions for any β while being still simple. They account both for the level repulsion in ∼s^β when s→0 and for the whole shape of the NNS distributions in the range of ‘s’ which is accessible to experiment or to most numerical simulations. The exact NNS distribution of the GOE (β=1) is in particular significantly better described by a generalized gamma distribution than it is by the Wigner surmise while the best generalized gamma approximation coincides essentially with the Wigner surmise for β>∼2. They describe too the evolution of the level repulsion between that of a Poisson distribution and that of a GOE distribution when β increases from 0 to 1. The distribution of ln (s), related to the electrostatic interaction energy between neighbouring charges, is accordingly well approximated by a generalized Gumbel distribution for any β?0. The distributions of the minimum NN spacing between eigenvalues of matrices from the β-HE, obtained both from as-calculated eigenvalues and from unfolded eigenvalues are Brody distributions which are classically used to characterize the spectral fluctuations of various physical systems.     

Influence of the weakly interacting light U boson on the properties of massive protoneutron stars

Considering the octet baryons in relativistic mean field theory and selecting entropy per baryon S=l,we calculate and discuss the influence of U bosons on the equation of state,mass-radius,moment of inertia and gravitational redshift of massive protoneutron stars(PNSs).The effective coupling constant gu of U bosons and nucleons is selected from 0 to 70 GeV~(-2).The results indicate that U bosons will stiffen the equation of state(EOS).The influence of U bosons on the pressure is more obvious at low density than high density,while the influence of U bosons on the energy density is more obvious at high density than low density.The U bosons play a significant role in increasing the maximum mass and radius of PNS.When the value of gu changes from 0 to 70 GeV~(-2),the maximum mass of a massive PNS increases from 2.11M_⊙ to 2.58M_⊙,and the radius of a PNS corresponding to PSR J0348+0432 increases from 13.71 km to 24.35 km.The U bosons will increase the moment of inertia and decrease the gravitational redshift of a PNS.For the PNS of the massive PSR J0348+0432,the radius and moment of inertia vary directly with gu,and the gravitational redshift varies approximately inversely with gu.     

交流源作用下介观RLC电路系统量子态随时间的演化

根据量子不变量理论，同时考虑介观电容器极板间电子波函数的耦合作用和电路的耗散,研究介观RLC电路系统在交流电流源作用下动力学的演化过程，并且得到描述系统量子态随时间的演化算符.进一步的分析结果表明，介观RLC电路系统的波函数将由任意的初态演化到一般的压缩态. 关键词： 介观RLC电路 交变电源 不变量理论 时间演化算符     

A Reliability Analysis of Calculated Results for Odd-Even and Odd-Odd Nuclei in Relativistic Mean-Field Theory

We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nuclei and odd-odd nuclei. We find that the errors of binding energy of odd-even and odd-odd nuclei are not bigger than the one of even-even nuclei. The result shows that comparing with even-even nuclei, there is no systematic error and approximation in the calculations of the binding energy of odd-even and odd-odd nuclei with relativistic mean-field theory. In addition,the result is explained theoretically.     

Persistence in financial markets

Persistence is studied in a financial context by mapping the time evolution of the values of the shares quoted on the London Financial Times Stock Exchange 100 index (FTSE 100) onto Ising spins. By following the time dependence of the spins, we find evidence for power law decay of the proportion of shares that remain either above or below their 'starting' values. As a result, we estimate a persistence exponent for the underlying financial market to be θ_f∼0.5.     

The dynamical properties of Rydberg hydrogen atom near a metal surface

The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided into vibrational and rotational region. Both the Poincaré surface of section and the closed orbit theory verify the same conclusion clearly. In this paper we choose the atomic principal quantum number asn=20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distanced. Whend is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system is integrable. Whend becomes smaller, there exists a critical valued _c. Ford>d _c, the system is near-integrable and the motion is regular. While chaotic motion appears ford<d _c, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the metal surface.     

Peripatetic Highlights in Bern

This tour of significant scientific sites in Bern uses the local legacy of its most illustrious scientists, Albert Einstein (1879–1955) and Fritz Houtermans (1903–1966), as its guiding thread through the old town and the university district.Ann M.Hentschel is translator of the correspondence volumes of The Collected Papers of Albert Einstein and is currently employed by the Institute for the History and Philosophy of Science at the University of Bern to write the guide for a city tour of Einsteins old haunts in Bern for the coming jubilee of special relativity in 2005. For the historical companion guidebook, see Hentschel and Grasshoff, Albert Einstein (ref. 4) and the website <.     

The effect of a permanent dipole moment on the polar molecule cavity quantum electrodynamics

A dressed-state perturbation theory beyond the rotating wave approximation(RWA) is presented to investigate the interaction between a two-level electronic transition of polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments(PDM) and the counter-rotating wave term(CRT) can be shown separately.The validity of these explicit results is discussed by comparison with the direct numerical simulation. Compared to the CRT coupling, PDM results in the coupling of more dressed states and the energy shift is proportional to the square of the normalized permanent dipole difference, and a greater Bloch–Siegert shift can be produced in the giant dipole molecule cavity QED. In addition, our method can also be extended to the solution of the two-level atom Rabi model Hamiltonian beyond the RWA.     

Phase transition and optoelectronic properties of MgH2

In this article, structural and electronic properties of MgH₂ have been studied. The aim behind this study was to find out the ground state crystal structure of MgH₂. For the purpose, density functional theory (DFT)-based full-potential linearized augmented plane wave (FP-LAPW) calculations have been performed in three different space groups: P4₂/mnm (α-MgH₂), Pa3 (β-MgH₂) and Pbcn (γ-MgH₂). It has been found that the ground state structure of MgH₂ is α-MgH₂. The present study shows that α-MgH₂ transforms into γ-MgH₂ at a pressure of 0.41 GPa. After further increase in pressure, γ-MgH₂ transforms into β-MgH₂ at a pressure of 3.67 GPa. The obtained results are in good agreement with previously reported experimental data. In all the studied phases, the behavior of MgH₂ is insulating and its optical conductivity is around 6.0 eV. The α-MgH₂ and γ-MgH₂ are anisotropic materials while β-MgH₂ is isotropic in nature.